We present a simple randomized algorithmic framework for connected facility location problems. The basic idea is as follows: We run a black-box approximation algorithm for the unconnected facility location problem, randomly sample the clients, and open the facilities serving sampled clients in the approximate solution. Via a novel analytical tool, which we term core detouring, we show that this approach significantly improves over the previously best known approximation ratios for several NP-hard network design problems. For example, we reduce the approximation ratio for the connected facility location problem from 8.55 to 4.00 and for the single-sink rent-or-buy problem from 3.55 to 2.92. The mentioned results can be derandomized at the expense of a slightly worse approximation ratio. The versatility of our framework is demonstrated by devising improved approximation algorithms also for other related problems. © 2010 Elsevier Inc. All rights reserved.
Eisenbrand, F., Grandoni, F., Rothvoß, T., & Schäfer, G. (2010). Connected facility location via random facility sampling and core detouring. Journal of Computer and System Sciences, 76(8), 709–726. https://doi.org/10.1016/j.jcss.2010.02.001